In the case of a combined hydraulic and pneumatic type of vehicle brake system, there is a possibility that when the vehicle wheels start rapidly again after a braking action is initiated in an anti-skid vehicle brake system, the wheel velocity will normally exceed the vehicle velocity. Such a case will generally occur every time during fast restarting of the vehicle wheels with acceleration values greater than 5 g. If the difference in velocities is great enough to set the deceleration stage for generation of the delay control signals, there is a risk of too early a drop in the brake pressure and hence, the reference velocity stage is set too early, i.e., the reference velocity runs out too soon, which involves the danger of underbraking the vehicle.